Why did Luxembourg become part of the German Confederation after 1815?

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Following the fall of Napoleon in 1814, the future of Luxembourg was determined by the allied powers at the Congress of Vienna in 1815.12

The congress elevated Luxembourg to the status of a grand duchy and granted it to William I, the king of the Netherlands, as a personal possession. As part of the geopolitical restructuring of Europe, the allied powers included the grand duchy within the German Confederation. This arrangement was further solidified by the great powers in 1831, who mandated that Luxembourg remain in William I’s possession while continuing to form part of the German Confederation. Additionally, a Prussian military garrison was stationed in the capital city to maintain this strategic presence.12